Title of the course: Sasakian geometry
Instructor: Doç. Dr. Craig van Coevering
Institution: Boğaziçi Üniversitesi
Dates: 6-18 January 2020
Prerequisites: Beginning graduate differential geometry, i.e. some knowledge of manifolds, Riemannian geometry, vector bundles, connections.
Level: Graduate
Abstract: This course will present some recent ideas in Sasakian geometry, with applications to Sasaki-Einstein manifolds, existence of constant scalar curvature and extremal metrics. In particular, we will discuss ideas involving complex geometry such as toric varieties, Hilbert series, and stability, with applications to the above special metrics. We will start with an introduction, which will only presuppose some knowledge of differential geometry. Then we will present recent topics involving the existence of special metrics, their obstructions, with applications to physics. And some recent topics involving complex geometry, Hilbert series, and K-stability.
Textbook and References:
1. Boyer, Charles P.;Galicki, Krzysztof. Sasakian geometry, Oxford Mathematical Monographs. Oxford University Press, Oxford, 2008.
2. Martelli, Dario; Sparks, James, Yau; Shing-Tung. The geometric dual of a-maximisation for toric Sasaki-Einstein manifolds, Comm. Math. Phys. 268 (2006), no. 1, 39–65.
3. Martelli, Dario; Sparks, James; Yau, Shing-Tung. Sasaki-Einstein manifolds and volume minimisation. Comm. Math. Phys. 280 (2008), no. 3, 611–673.
4. Collins, Tristan C.; Székelyhidi, Gábor. K-semistability for irregular Sasakian manifolds. J. Differential Geom. 109 (2018), no. 1, 81–109.
5. Collins, Tristan C.; Székelyhidi, Gábor. Sasaki-Einstein metrics and K-stability. Geom. Topol. 23 (2019), no. 3, 1339–1413.
Language: EN